LMFDB - Embedded newform 405.2.r.a.332.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			332.16
Character	$\chi$	$=$	405.332
Dual form			405.2.r.a.233.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52658 + 2.18018i) q^{2} +(-1.73870 + 4.77703i) q^{4} +(1.77382 - 1.36146i) q^{5} +(2.78918 + 1.30062i) q^{7} +(-7.92739 + 2.12414i) q^{8} +(5.67609 + 1.78885i) q^{10} +(0.426793 - 0.508631i) q^{11} +(0.384347 + 0.269123i) q^{13} +(1.42232 + 8.06640i) q^{14} +(-8.94423 - 7.50510i) q^{16} +(-4.50051 - 1.20591i) q^{17} +(-4.80938 - 2.77670i) q^{19} +(3.41962 + 10.8407i) q^{20} +(1.76044 + 0.154018i) q^{22} +(-0.0280775 - 0.0602123i) q^{23} +(1.29284 - 4.82997i) q^{25} +1.24878i q^{26} +(-11.0626 + 11.0626i) q^{28} +(0.434735 - 2.46551i) q^{29} +(1.76652 + 0.642961i) q^{31} +(1.27781 - 14.6055i) q^{32} +(-4.24128 - 11.6528i) q^{34} +(6.71823 - 1.49031i) q^{35} +(0.656295 - 2.44933i) q^{37} +(-1.28820 - 14.7241i) q^{38} +(-11.1698 + 14.5607i) q^{40} +(-1.62695 + 0.286875i) q^{41} +(8.36925 - 0.732214i) q^{43} +(1.68769 + 2.92316i) q^{44} +(0.0884111 - 0.153133i) q^{46} +(-1.73166 + 3.71355i) q^{47} +(1.58841 + 1.89299i) q^{49} +(12.5038 - 4.55469i) q^{50} +(-1.95387 + 1.36812i) q^{52} +(7.52870 + 7.52870i) q^{53} +(0.0645683 - 1.48328i) q^{55} +(-24.8736 - 4.38589i) q^{56} +(6.03890 - 2.81598i) q^{58} +(-3.49452 + 2.93225i) q^{59} +(-5.84534 + 2.12753i) q^{61} +(1.29496 + 4.83286i) q^{62} +(13.5701 - 7.83468i) q^{64} +(1.04816 - 0.0459001i) q^{65} +(3.13881 - 4.48268i) q^{67} +(13.5857 - 19.4024i) q^{68} +(13.5050 + 12.3719i) q^{70} +(5.33043 - 3.07752i) q^{71} +(-3.64803 - 13.6146i) q^{73} +(6.34185 - 2.30824i) q^{74} +(21.6264 - 18.1467i) q^{76} +(1.85194 - 0.863572i) q^{77} +(5.34198 + 0.941936i) q^{79} +(-26.0833 - 1.13543i) q^{80} +(-3.10910 - 3.10910i) q^{82} +(-4.64599 + 3.25316i) q^{83} +(-9.62487 + 3.98822i) q^{85} +(14.3727 + 17.1287i) q^{86} +(-2.30295 + 4.93869i) q^{88} +(-3.08131 + 5.33699i) q^{89} +(0.721988 + 1.25052i) q^{91} +(0.336454 - 0.0294359i) q^{92} +(-10.7397 + 1.89370i) q^{94} +(-12.3113 + 1.62244i) q^{95} +(-1.18828 - 13.5821i) q^{97} +(-1.70223 + 6.35281i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.52658	+	2.18018i	1.07945	+	1.54162i	0.816969	+	0.576682i	$0.195653\pi$
$2$	1.52658	+	2.18018i	1.07945	+	1.54162i	0.262484	+	0.964936i	$0.415458\pi$
$3$		0			0
$3$		0			0
$4$	−1.73870	+	4.77703i	−0.869348	+	2.38851i
$5$	1.77382	−	1.36146i	0.793274	−	0.608864i
$5$	1.77382	−	1.36146i	0.793274	−	0.608864i
$6$		0			0
$7$	2.78918	+	1.30062i	1.05421	+	0.491587i	0.870896	−	0.491468i	$-0.163539\pi$
$7$	2.78918	+	1.30062i	1.05421	+	0.491587i	0.183315	+	0.983054i	$0.441317\pi$
$8$	−7.92739	+	2.12414i	−2.80276	+	0.750996i
$9$		0			0
$10$	5.67609	+	1.78885i	1.79494	+	0.565686i
$11$	0.426793	−	0.508631i	0.128683	−	0.153358i	−0.697856	−	0.716238i	$-0.745862\pi$
$11$	0.426793	−	0.508631i	0.128683	−	0.153358i	0.826538	+	0.562880i	$0.190307\pi$
$12$		0			0
$13$	0.384347	+	0.269123i	0.106599	+	0.0746412i	0.625660	−	0.780096i	$-0.284830\pi$
$13$	0.384347	+	0.269123i	0.106599	+	0.0746412i	−0.519062	+	0.854737i	$0.673718\pi$
$14$	1.42232	+	8.06640i	0.380132	+	2.15584i
$15$		0			0
$16$	−8.94423	−	7.50510i	−2.23606	−	1.87627i
$17$	−4.50051	−	1.20591i	−1.09153	−	0.292476i	−0.332221	−	0.943201i	$-0.607798\pi$
$17$	−4.50051	−	1.20591i	−1.09153	−	0.292476i	−0.759313	+	0.650726i	$0.774465\pi$
$18$		0			0
$19$	−4.80938	−	2.77670i	−1.10335	−	0.637018i	−0.166249	−	0.986084i	$-0.553166\pi$
$19$	−4.80938	−	2.77670i	−1.10335	−	0.637018i	−0.937098	+	0.349066i	$0.886499\pi$
$20$	3.41962	+	10.8407i	0.764650	+	2.42406i
$21$		0			0
$22$	1.76044	+	0.154018i	0.375327	+	0.0328368i
$23$	−0.0280775	−	0.0602123i	−0.00585456	−	0.0125551i	0.903359	−	0.428886i	$-0.141094\pi$
$23$	−0.0280775	−	0.0602123i	−0.00585456	−	0.0125551i	−0.909213	+	0.416331i	$0.863316\pi$
$24$		0			0
$25$	1.29284	−	4.82997i	0.258568	−	0.965993i
$26$			1.24878i			0.244906i
$27$		0			0
$28$	−11.0626	+	11.0626i	−2.09064	+	2.09064i
$29$	0.434735	−	2.46551i	0.0807283	−	0.457833i	−0.917469	−	0.397808i	$-0.869771\pi$
$29$	0.434735	−	2.46551i	0.0807283	−	0.457833i	0.998197	−	0.0600247i	$-0.0191180\pi$
$30$		0			0
$31$	1.76652	+	0.642961i	0.317276	+	0.115479i	0.495749	−	0.868466i	$-0.334893\pi$
$31$	1.76652	+	0.642961i	0.317276	+	0.115479i	−0.178473	+	0.983945i	$0.557116\pi$
$32$	1.27781	−	14.6055i	0.225888	−	2.58191i
$33$		0			0
$34$	−4.24128	−	11.6528i	−0.727373	−	1.99844i
$35$	6.71823	−	1.49031i	1.13559	−	0.251909i
$36$		0			0
$37$	0.656295	−	2.44933i	0.107894	−	0.402667i	−0.890763	−	0.454468i	$-0.849830\pi$
$37$	0.656295	−	2.44933i	0.107894	−	0.402667i	0.998657	+	0.0518010i	$0.0164962\pi$
$38$	−1.28820	−	14.7241i	−0.208973	−	2.38857i
$39$		0			0
$40$	−11.1698	+	14.5607i	−1.76610	+	2.30224i
$41$	−1.62695	+	0.286875i	−0.254087	+	0.0448023i	−0.299241	−	0.954178i	$-0.596733\pi$
$41$	−1.62695	+	0.286875i	−0.254087	+	0.0448023i	0.0451539	+	0.998980i	$0.485622\pi$
$42$		0			0
$43$	8.36925	−	0.732214i	1.27630	−	0.111662i	0.571224	−	0.820794i	$-0.306469\pi$
$43$	8.36925	−	0.732214i	1.27630	−	0.111662i	0.705075	+	0.709133i	$0.250913\pi$
$44$	1.68769	+	2.92316i	0.254428	+	0.440682i
$45$		0			0
$46$	0.0884111	−	0.153133i	0.0130355	−	0.0225782i
$47$	−1.73166	+	3.71355i	−0.252588	+	0.541677i	−0.991187	−	0.132468i	$-0.957710\pi$
$47$	−1.73166	+	3.71355i	−0.252588	+	0.541677i	0.738599	+	0.674145i	$0.235488\pi$
$48$		0			0
$49$	1.58841	+	1.89299i	0.226916	+	0.270428i
$50$	12.5038	−	4.55469i	1.76830	−	0.644131i
$51$		0			0
$52$	−1.95387	+	1.36812i	−0.270953	+	0.189723i
$53$	7.52870	+	7.52870i	1.03415	+	1.03415i	0.999396	+	0.0347509i	$0.0110638\pi$
$53$	7.52870	+	7.52870i	1.03415	+	1.03415i	0.0347509	+	0.999396i	$0.488936\pi$
$54$		0			0
$55$	0.0645683	−	1.48328i	0.00870639	−	0.200005i
$56$	−24.8736	−	4.38589i	−3.32388	−	0.586089i
$57$		0			0
$58$	6.03890	−	2.81598i	0.792946	−	0.369757i
$59$	−3.49452	+	2.93225i	−0.454948	+	0.381747i	−0.841268	−	0.540618i	$-0.818190\pi$
$59$	−3.49452	+	2.93225i	−0.454948	+	0.381747i	0.386320	+	0.922365i	$0.373746\pi$
$60$		0			0
$61$	−5.84534	+	2.12753i	−0.748419	+	0.272402i	−0.687940	−	0.725767i	$-0.741485\pi$
$61$	−5.84534	+	2.12753i	−0.748419	+	0.272402i	−0.0604785	+	0.998169i	$0.519263\pi$
$62$	1.29496	+	4.83286i	0.164460	+	0.613773i
$63$		0			0
$64$	13.5701	−	7.83468i	1.69626	−	0.979335i
$65$	1.04816	−	0.0459001i	0.130008	−	0.00569321i
$66$		0			0
$67$	3.13881	−	4.48268i	0.383466	−	0.547646i	−0.580297	−	0.814405i	$-0.697064\pi$
$67$	3.13881	−	4.48268i	0.383466	−	0.547646i	0.963763	+	0.266758i	$0.0859525\pi$
$68$	13.5857	−	19.4024i	1.64751	−	2.35288i
$69$		0			0
$70$	13.5050	+	12.3719i	1.61416	+	1.47872i
$71$	5.33043	−	3.07752i	0.632605	−	0.365235i	−0.149155	−	0.988814i	$-0.547655\pi$
$71$	5.33043	−	3.07752i	0.632605	−	0.365235i	0.781760	+	0.623579i	$0.214322\pi$
$72$		0			0
$73$	−3.64803	−	13.6146i	−0.426970	−	1.59347i	−0.759583	−	0.650410i	$-0.774597\pi$
$73$	−3.64803	−	13.6146i	−0.426970	−	1.59347i	0.332613	−	0.943063i	$-0.392070\pi$
$74$	6.34185	−	2.30824i	0.737225	−	0.268328i
$75$		0			0
$76$	21.6264	−	18.1467i	2.48072	−	2.08157i
$77$	1.85194	−	0.863572i	0.211048	−	0.0984131i
$78$		0			0
$79$	5.34198	+	0.941936i	0.601020	+	0.105976i	0.465876	−	0.884850i	$-0.345739\pi$
$79$	5.34198	+	0.941936i	0.601020	+	0.105976i	0.135144	+	0.990826i	$0.456850\pi$
$80$	−26.0833	−	1.13543i	−2.91620	−	0.126945i
$81$		0			0
$82$	−3.10910	−	3.10910i	−0.343343	−	0.343343i
$83$	−4.64599	+	3.25316i	−0.509964	+	0.357081i	−0.800063	−	0.599916i	$-0.795201\pi$
$83$	−4.64599	+	3.25316i	−0.509964	+	0.357081i	0.290099	+	0.956997i	$0.406312\pi$
$84$		0			0
$85$	−9.62487	+	3.98822i	−1.04396	+	0.432583i
$86$	14.3727	+	17.1287i	1.54984	+	1.84703i
$87$		0			0
$88$	−2.30295	+	4.93869i	−0.245495	+	0.526466i
$89$	−3.08131	+	5.33699i	−0.326619	+	0.565720i	−0.981839	−	0.189718i	$-0.939243\pi$
$89$	−3.08131	+	5.33699i	−0.326619	+	0.565720i	0.655220	+	0.755438i	$0.272576\pi$
$90$		0			0
$91$	0.721988	+	1.25052i	0.0756849	+	0.131090i
$92$	0.336454	−	0.0294359i	0.0350778	−	0.00306891i
$93$		0			0
$94$	−10.7397	+	1.89370i	−1.10772	+	0.195320i
$95$	−12.3113	+	1.62244i	−1.26312	+	0.166459i
$96$		0			0
$97$	−1.18828	−	13.5821i	−0.120652	−	1.37906i	−0.779321	−	0.626625i	$-0.784436\pi$
$97$	−1.18828	−	13.5821i	−0.120652	−	1.37906i	0.658669	−	0.752433i	$-0.271120\pi$
$98$	−1.70223	+	6.35281i	−0.171951	+	0.641731i
$99$		0			0
$100$	20.8250	+	14.5738i	2.08250	+	1.45738i
$101$	0.629841	+	1.73048i	0.0626716	+	0.172189i	0.967076	−	0.254487i	$-0.0819067\pi$
$101$	0.629841	+	1.73048i	0.0626716	+	0.172189i	−0.904405	+	0.426676i	$0.859684\pi$
$102$		0			0
$103$	−1.42347	+	16.2704i	−0.140259	+	1.60317i	0.521368	+	0.853332i	$0.325422\pi$
$103$	−1.42347	+	16.2704i	−0.140259	+	1.60317i	−0.661627	+	0.749833i	$0.730134\pi$
$104$	−3.61852	−	1.31704i	−0.354826	−	0.129146i
$105$		0			0
$106$	−4.92077	+	27.9071i	−0.477947	+	2.71057i
$107$	10.4880	−	10.4880i	1.01391	−	1.01391i	0.0140087	−	0.999902i	$-0.495541\pi$
$107$	10.4880	−	10.4880i	1.01391	−	1.01391i	0.999902	−	0.0140087i	$-0.00445924\pi$
$108$		0			0
$109$			9.34913i			0.895484i	0.894163	+	0.447742i	$0.147772\pi$
$109$			9.34913i			0.895484i	−0.894163	+	0.447742i	$0.852228\pi$
$110$	3.33238	−	2.12357i	0.317730	−	0.202474i
$111$		0			0
$112$	−15.1858	−	32.5661i	−1.43492	−	3.07721i
$113$	−20.6993	−	1.81095i	−1.94722	−	0.170360i	−0.955159	−	0.296094i	$-0.904316\pi$
$113$	−20.6993	−	1.81095i	−1.94722	−	0.170360i	−0.992064	+	0.125734i	$0.959871\pi$
$114$		0			0
$115$	−0.131781	−	0.0685791i	−0.0122886	−	0.00639504i
$116$	11.0219	+	6.36351i	1.02336	+	0.590837i
$117$		0			0
$118$	−11.7275	−	3.14237i	−1.07960	−	0.289278i
$119$	−10.9843	−	9.21693i	−1.00693	−	0.844915i
$120$		0			0
$121$	1.83358	+	10.3987i	0.166689	+	0.945339i
$122$	−13.5617	−	9.49604i	−1.22782	−	0.859731i
$123$		0			0
$124$	−6.14289	+	7.32081i	−0.551648	+	0.657428i
$125$	−4.28256	−	10.3276i	−0.383043	−	0.923730i
$126$		0			0
$127$	7.35416	−	1.97054i	0.652576	−	0.174857i	0.0826829	−	0.996576i	$-0.473651\pi$
$127$	7.35416	−	1.97054i	0.652576	−	0.174857i	0.569893	+	0.821719i	$0.306984\pi$
$128$	11.2214	+	5.23265i	0.991845	+	0.462505i
$129$		0			0
$130$	1.70017	+	2.21511i	0.149115	+	0.194278i
$131$	−4.01388	+	11.0280i	−0.350694	+	0.963524i	0.631454	+	0.775414i	$0.282459\pi$
$131$	−4.01388	+	11.0280i	−0.350694	+	0.963524i	−0.982148	+	0.188111i	$0.939764\pi$
$132$		0			0
$133$	−9.80281	−	13.9999i	−0.850012	−	1.21394i
$134$	14.5647			1.25820
$135$		0			0
$136$	38.2388			3.27895
$137$	−3.85643	−	5.50755i	−0.329477	−	0.470542i	0.619900	−	0.784681i	$-0.287173\pi$
$137$	−3.85643	−	5.50755i	−0.329477	−	0.470542i	−0.949377	+	0.314139i	$0.898284\pi$
$138$		0			0
$139$	0.519349	−	1.42690i	0.0440506	−	0.121028i	−0.915717	−	0.401824i	$-0.868376\pi$
$139$	0.519349	−	1.42690i	0.0440506	−	0.121028i	0.959767	+	0.280796i	$0.0905985\pi$
$140$	−4.56170	+	34.6844i	−0.385534	+	2.93137i
$141$		0			0
$142$	14.8468	+	6.92320i	1.24592	+	0.580982i
$143$	0.300921	−	0.0806315i	0.0251643	−	0.00674274i
$144$		0			0
$145$	−2.58555	−	4.96523i	−0.214719	−	0.412340i
$146$	24.1133	−	28.7372i	1.99563	−	2.37830i
$147$		0			0
$148$	10.5594	+	7.39377i	0.867978	+	0.607764i
$149$	3.69731	+	20.9685i	0.302895	+	1.71780i	0.633250	+	0.773947i	$0.281720\pi$
$149$	3.69731	+	20.9685i	0.302895	+	1.71780i	−0.330355	+	0.943857i	$0.607168\pi$
$150$		0			0
$151$	6.08208	+	5.10347i	0.494952	+	0.415314i	0.855797	−	0.517312i	$-0.173067\pi$
$151$	6.08208	+	5.10347i	0.494952	+	0.415314i	−0.360845	+	0.932626i	$0.617512\pi$
$152$	44.0239	+	11.7962i	3.57081	+	0.956797i
$153$		0			0
$154$	4.70986	+	2.71924i	0.379531	+	0.219123i
$155$	4.00885	−	1.26456i	0.321998	−	0.101572i
$156$		0			0
$157$	−13.6200	−	1.19160i	−1.08699	−	0.0950997i	−0.470455	−	0.882424i	$-0.655910\pi$
$157$	−13.6200	−	1.19160i	−1.08699	−	0.0950997i	−0.616539	+	0.787324i	$0.711466\pi$
$158$	6.10136	+	13.0844i	0.485398	+	1.04094i
$159$		0			0
$160$	−17.6182	−	27.6471i	−1.39284	−	2.18570i
$161$		−	0.204461i		−	0.0161138i
$162$		0			0
$163$	13.8462	−	13.8462i	1.08452	−	1.08452i	0.0884330	−	0.996082i	$-0.471814\pi$
$163$	13.8462	−	13.8462i	1.08452	−	1.08452i	0.996082	−	0.0884330i	$-0.0281859\pi$
$164$	1.45836	−	8.27077i	0.113879	−	0.645839i
$165$		0			0
$166$	−14.1849	−	5.16289i	−1.10096	−	0.400718i
$167$	1.91506	−	21.8892i	0.148192	−	1.69384i	−0.450435	−	0.892809i	$-0.648731\pi$
$167$	1.91506	−	21.8892i	0.148192	−	1.69384i	0.598627	−	0.801028i	$-0.295713\pi$
$168$		0			0
$169$	−4.37097	−	12.0091i	−0.336228	−	0.923779i
$170$	−23.3881	−	14.8956i	−1.79379	−	1.14244i
$171$		0			0
$172$	−11.0538	+	41.2533i	−0.842842	+	3.14553i
$173$	0.327061	+	3.73833i	0.0248660	+	0.284220i	0.998439	+	0.0558456i	$0.0177854\pi$
$173$	0.327061	+	3.73833i	0.0248660	+	0.284220i	−0.973573	+	0.228374i	$0.926659\pi$
$174$		0			0
$175$	9.88789	−	11.7902i	0.747455	−	0.891252i
$176$	−7.63466	+	1.34620i	−0.575484	+	0.101473i
$177$		0			0
$178$	−16.3394	+	1.42952i	−1.22469	+	0.107147i
$179$	−7.21345	−	12.4941i	−0.539158	−	0.933850i	−0.998950	−	0.0458226i	$-0.985409\pi$
$179$	−7.21345	−	12.4941i	−0.539158	−	0.933850i	0.459791	−	0.888027i	$-0.347924\pi$
$180$		0			0
$181$	−7.06370	+	12.2347i	−0.525041	+	0.909397i	0.474534	+	0.880237i	$0.342617\pi$
$181$	−7.06370	+	12.2347i	−0.525041	+	0.909397i	−0.999575	+	0.0291599i	$0.990717\pi$
$182$	−1.62419	+	3.48308i	−0.120393	+	0.258183i
$183$		0			0
$184$	0.350480	+	0.417686i	0.0258378	+	0.0307922i
$185$	−2.17052	−	5.23817i	−0.159580	−	0.385118i
$186$		0			0
$187$	−2.53415	+	1.77443i	−0.185315	+	0.129759i
$188$	−14.7289	−	14.7289i	−1.07422	−	1.07422i
$189$		0			0
$190$	−22.3314	−	24.3641i	−1.62009	−	1.76756i
$191$	2.54718	+	0.449136i	0.184307	+	0.0324983i	0.265040	−	0.964237i	$-0.414615\pi$
$191$	2.54718	+	0.449136i	0.184307	+	0.0324983i	−0.0807326	+	0.996736i	$0.525726\pi$
$192$		0			0
$193$	−12.9195	+	6.02445i	−0.929963	+	0.433649i	−0.827740	−	0.561112i	$-0.810374\pi$
$193$	−12.9195	+	6.02445i	−0.929963	+	0.433649i	−0.102224	+	0.994761i	$0.532596\pi$
$194$	27.7975	−	23.3248i	1.99574	−	1.67463i
$195$		0			0
$196$	−11.8046	+	4.29654i	−0.843189	+	0.306896i
$197$	2.16013	+	8.06170i	0.153903	+	0.574372i	0.999197	+	0.0400711i	$0.0127585\pi$
$197$	2.16013	+	8.06170i	0.153903	+	0.574372i	−0.845294	+	0.534301i	$0.820575\pi$
$198$		0			0
$199$	−3.27312	+	1.88973i	−0.232025	+	0.133960i	−0.611506	−	0.791240i	$-0.709436\pi$
$199$	−3.27312	+	1.88973i	−0.232025	+	0.133960i	0.379481	+	0.925200i	$0.376103\pi$
$200$	0.0106623	+	41.0352i	0.000753936	+	2.90163i
$201$		0			0
$202$	−2.81124	+	4.01487i	−0.197798	+	0.282485i
$203$	4.41923	−	6.31132i	0.310169	−	0.442968i
$204$		0			0
$205$	−2.49534	+	2.72389i	−0.174282	+	0.190245i
$206$	−37.6453	+	21.7345i	−2.62287	+	1.51432i
$207$		0			0
$208$	−1.41790	−	5.29166i	−0.0983134	−	0.366911i
$209$	−3.46492	+	1.26113i	−0.239674	+	0.0872341i
$210$		0			0
$211$	−13.6392	+	11.4447i	−0.938964	+	0.787885i	−0.977405	−	0.211376i	$-0.932205\pi$
$211$	−13.6392	+	11.4447i	−0.938964	+	0.787885i	0.0384403	+	0.999261i	$0.487761\pi$
$212$	−49.0550	+	22.8747i	−3.36911	+	1.57104i
$213$		0			0
$214$	38.8763	+	6.85495i	2.65753	+	0.468594i
$215$	13.8486	−	12.6932i	0.944468	−	0.865671i
$216$		0			0
$217$	4.09090	+	4.09090i	0.277708	+	0.277708i
$218$	−20.3828	+	14.2722i	−1.38049	+	0.966633i
$219$		0			0
$220$	6.97341	+	2.88742i	0.470147	+	0.194670i
$221$	−1.40522	−	1.67468i	−0.0945254	−	0.112651i
$222$		0			0
$223$	−8.09113	+	17.3515i	−0.541822	+	1.16194i	0.424694	+	0.905337i	$0.360382\pi$
$223$	−8.09113	+	17.3515i	−0.541822	+	1.16194i	−0.966516	+	0.256605i	$0.917396\pi$
$224$	22.5602	−	39.0754i	1.50737	−	2.61083i
$225$		0			0
$226$	−27.6508	−	47.8926i	−1.83930	−	3.18577i
$227$	−0.480953	+	0.0420779i	−0.0319220	+	0.00279281i	−0.103106	−	0.994670i	$-0.532878\pi$
$227$	−0.480953	+	0.0420779i	−0.0319220	+	0.00279281i	0.0711836	+	0.997463i	$0.477322\pi$
$228$		0			0
$229$	−14.7979	+	2.60927i	−0.977875	+	0.172426i	−0.639672	−	0.768648i	$-0.720930\pi$
$229$	−14.7979	+	2.60927i	−0.977875	+	0.172426i	−0.338203	+	0.941073i	$0.609819\pi$
$230$	−0.0516592	−	0.391997i	−0.00340631	−	0.0258475i
$231$		0			0
$232$	1.79076	+	20.4685i	0.117569	+	1.34382i
$233$	0.143242	−	0.534587i	0.00938411	−	0.0350220i	−0.961075	−	0.276287i	$-0.910896\pi$
$233$	0.143242	−	0.534587i	0.00938411	−	0.0350220i	0.970459	+	0.241266i	$0.0775625\pi$
$234$		0			0
$235$	1.98422	+	8.94473i	0.129436	+	0.583490i
$236$	−7.93154	−	21.7917i	−0.516299	−	1.41852i
$237$		0			0
$238$	3.32615	−	38.0181i	0.215602	−	2.46435i
$239$	−5.32354	−	1.93761i	−0.344351	−	0.125334i	0.164054	−	0.986451i	$-0.447543\pi$
$239$	−5.32354	−	1.93761i	−0.344351	−	0.125334i	−0.508406	+	0.861118i	$0.669765\pi$
$240$		0			0
$241$	0.317967	−	1.80328i	0.0204821	−	0.116160i	−0.972853	−	0.231426i	$-0.925661\pi$
$241$	0.317967	−	1.80328i	0.0204821	−	0.116160i	0.993335	+	0.115266i	$0.0367721\pi$
$242$	−19.8720	+	19.8720i	−1.27742	+	1.27742i
$243$		0			0
$244$		−	31.6225i		−	2.02442i
$245$	5.39478	+	1.19526i	0.344660	+	0.0763623i
$246$		0			0
$247$	−1.10120	−	2.36153i	−0.0700677	−	0.150261i
$248$	−15.3696	−	1.34467i	−0.975973	−	0.0853866i
$249$		0			0
$250$	15.9784	−	25.1026i	1.01056	−	1.58763i
$251$	16.8470	+	9.72663i	1.06337	+	0.613939i	0.926364	−	0.376630i	$-0.122917\pi$
$251$	16.8470	+	9.72663i	1.06337	+	0.613939i	0.137011	+	0.990570i	$0.456251\pi$
$252$		0			0
$253$	−0.0426091	−	0.0114171i	−0.00267881	−	0.000717786i
$254$	15.5228	+	13.0252i	0.973988	+	0.817273i
$255$		0			0
$256$	0.280392	+	1.59018i	0.0175245	+	0.0993864i
$257$	24.5109	+	17.1627i	1.52895	+	1.07058i	0.970518	+	0.241027i	$0.0774842\pi$
$257$	24.5109	+	17.1627i	1.52895	+	1.07058i	0.558428	+	0.829553i	$0.311405\pi$
$258$		0			0
$259$	5.01616	−	5.97802i	0.311689	−	0.371456i
$260$	−1.60317	+	5.08690i	−0.0994243	+	0.315476i
$261$		0			0
$262$	−30.1706	+	8.08418i	−1.86394	+	0.499442i
$263$	−7.60797	−	3.54766i	−0.469128	−	0.218758i	0.173655	−	0.984807i	$-0.444442\pi$
$263$	−7.60797	−	3.54766i	−0.469128	−	0.218758i	−0.642782	+	0.766049i	$0.722220\pi$
$264$		0			0
$265$	23.6046	+	3.10448i	1.45002	+	0.190707i
$266$	15.5574	−	42.7437i	0.953888	−	2.62079i
$267$		0			0
$268$	15.9565	+	22.7882i	0.974696	+	1.39201i
$269$	−2.21545			−0.135079			−0.0675393	−	0.997717i	$-0.521515\pi$
$269$	−2.21545			−0.135079			−0.0675393	+	0.997717i	$0.521515\pi$
$270$		0			0
$271$	−5.87725			−0.357017			−0.178509	−	0.983938i	$-0.557127\pi$
$271$	−5.87725			−0.357017			−0.178509	+	0.983938i	$0.557127\pi$
$272$	31.2031	+	44.5627i	1.89197	+	2.70201i
$273$		0			0
$274$	6.12031	−	16.8154i	0.369741	−	1.01586i
$275$	−1.90490	−	2.71897i	−0.114870	−	0.163960i
$276$		0			0
$277$	10.2541	+	4.78156i	0.616108	+	0.287296i	0.705510	−	0.708700i	$-0.250718\pi$
$277$	10.2541	+	4.78156i	0.616108	+	0.287296i	−0.0894020	+	0.995996i	$0.528496\pi$
$278$	3.90372	−	1.04600i	0.234130	−	0.0627348i
$279$		0			0
$280$	−50.0924	+	26.0847i	−2.99359	+	1.55886i
$281$	−13.9719	+	16.6511i	−0.833496	+	0.993322i	0.166478	+	0.986045i	$0.446761\pi$
$281$	−13.9719	+	16.6511i	−0.833496	+	0.993322i	−0.999974	+	0.00727642i	$0.997684\pi$
$282$		0			0
$283$	10.7514	+	7.52820i	0.639103	+	0.447505i	0.847685	−	0.530500i	$-0.177996\pi$
$283$	10.7514	+	7.52820i	0.639103	+	0.447505i	−0.208582	+	0.978005i	$0.566885\pi$
$284$	5.43342	+	30.8145i	0.322414	+	1.82850i
$285$		0			0
$286$	0.635170	+	0.532971i	0.0375584	+	0.0315152i
$287$	−4.91097	−	1.31589i	−0.289885	−	0.0776745i
$288$		0			0
$289$	4.07794	+	2.35440i	0.239879	+	0.138494i
$290$	6.87803	−	13.2168i	0.403892	−	0.776115i
$291$		0			0
$292$	71.3804	+	6.24497i	4.17722	+	0.365460i
$293$	−1.80181	−	3.86399i	−0.105263	−	0.225736i	0.846621	−	0.532196i	$-0.178633\pi$
$293$	−1.80181	−	3.86399i	−0.105263	−	0.225736i	−0.951884	+	0.306460i	$0.900855\pi$
$294$		0			0
$295$	−2.20648	+	9.95893i	−0.128466	+	0.579831i
$296$			20.8108i			1.20960i
$297$		0			0
$298$	−40.0708	+	40.0708i	−2.32124	+	2.32124i
$299$	0.00541301	−	0.0306987i	0.000313043	−	0.00177535i
$300$		0			0
$301$	24.2957	+	8.84290i	1.40038	+	0.509696i
$302$	−1.84171	+	21.0508i	−0.105978	+	1.21134i
$303$		0			0
$304$	22.1768	+	60.9303i	1.27193	+	3.49459i
$305$	−7.47200	+	11.7320i	−0.427845	+	0.671775i
$306$		0			0
$307$	−4.82189	+	17.9955i	−0.275200	+	1.02706i	0.680508	+	0.732741i	$0.261759\pi$
$307$	−4.82189	+	17.9955i	−0.275200	+	1.02706i	−0.955707	+	0.294318i	$0.904907\pi$
$308$	0.905354	+	10.3482i	0.0515873	+	0.589646i
$309$		0			0
$310$	8.87677	+	6.80956i	0.504167	+	0.386757i
$311$	8.07539	−	1.42391i	0.457913	−	0.0807425i	0.0600667	−	0.998194i	$-0.480869\pi$
$311$	8.07539	−	1.42391i	0.457913	−	0.0807425i	0.397847	+	0.917452i	$0.369758\pi$
$312$		0			0
$313$	−18.9940	+	1.66176i	−1.07360	+	0.0939283i	−0.610222	−	0.792230i	$-0.708920\pi$
$313$	−18.9940	+	1.66176i	−1.07360	+	0.0939283i	−0.463382	+	0.886158i	$0.653364\pi$
$314$	−18.1941	−	31.5131i	−1.02675	−	1.77839i
$315$		0			0
$316$	−13.7877	+	23.8811i	−0.775621	+	1.34342i
$317$	7.17642	−	15.3899i	0.403068	−	0.864382i	−0.595087	−	0.803661i	$-0.702882\pi$
$317$	7.17642	−	15.3899i	0.403068	−	0.864382i	0.998155	−	0.0607206i	$-0.0193399\pi$
$318$		0			0
$319$	−1.06849	−	1.27338i	−0.0598241	−	0.0712956i
$320$	13.4042	−	32.3724i	0.749315	−	1.80967i
$321$		0			0
$322$	0.445761	−	0.312125i	0.0248413	−	0.0173941i
$323$	18.2962	+	18.2962i	1.01803	+	1.01803i
$324$		0			0
$325$	1.79675	−	1.50845i	0.0996659	−	0.0836738i
$326$	51.3243	+	9.04986i	2.84259	+	0.501225i
$327$		0			0
$328$	12.2881	−	5.73003i	0.678497	−	0.316388i
$329$	−9.65980	+	8.10554i	−0.532562	+	0.446873i
$330$		0			0
$331$	13.3657	−	4.86470i	0.734643	−	0.267388i	0.0525142	−	0.998620i	$-0.483277\pi$
$331$	13.3657	−	4.86470i	0.734643	−	0.267388i	0.682129	+	0.731232i	$0.261054\pi$
$332$	−7.46247	−	27.8503i	−0.409556	−	1.52848i
$333$		0			0
$334$	50.6458	−	29.2404i	2.77122	−	1.59996i
$335$	−0.535338	−	12.2248i	−0.0292486	−	0.667913i
$336$		0			0
$337$	−3.90887	+	5.58245i	−0.212930	+	0.304095i	−0.911382	−	0.411561i	$-0.864984\pi$
$337$	−3.90887	+	5.58245i	−0.212930	+	0.304095i	0.698452	+	0.715657i	$0.253872\pi$
$338$	19.5094	−	27.8623i	1.06117	−	1.51551i
$339$		0			0
$340$	−2.31710	−	52.9126i	−0.125662	−	2.86959i
$341$	1.08097	−	0.624097i	0.0585377	−	0.0337968i
$342$		0			0
$343$	−3.60734	−	13.4628i	−0.194778	−	0.726922i
$344$	−64.7910	+	23.5820i	−3.49330	+	1.27146i
$345$		0			0
$346$	−7.65094	+	6.41990i	−0.411317	+	0.345136i
$347$	12.4642	−	5.81216i	0.669114	−	0.312013i	−0.0582130	−	0.998304i	$-0.518540\pi$
$347$	12.4642	−	5.81216i	0.669114	−	0.312013i	0.727327	+	0.686291i	$0.240762\pi$
$348$		0			0
$349$	−26.3484	−	4.64594i	−1.41040	−	0.248691i	−0.583990	−	0.811761i	$-0.698509\pi$
$349$	−26.3484	−	4.64594i	−1.41040	−	0.248691i	−0.826409	+	0.563070i	$0.809620\pi$
$350$	40.7993	+	3.55879i	2.18081	+	0.190225i
$351$		0			0
$352$	−6.88345	−	6.88345i	−0.366889	−	0.366889i
$353$	0.0387563	−	0.0271374i	0.00206279	−	0.00144438i	−0.572545	−	0.819874i	$-0.694044\pi$
$353$	0.0387563	−	0.0271374i	0.00206279	−	0.00144438i	0.574607	+	0.818429i	$0.305155\pi$
$354$		0			0
$355$	5.26526	−	12.7161i	0.279451	−	0.674902i
$356$	−20.1375	−	23.9989i	−1.06729	−	1.27194i
$357$		0			0
$358$	16.2274	−	34.7997i	0.857644	−	1.83922i
$359$	−9.42597	+	16.3263i	−0.497484	+	0.861667i	−0.999996	−	0.00290290i	$-0.999076\pi$
$359$	−9.42597	+	16.3263i	−0.497484	+	0.861667i	0.502512	+	0.864570i	$0.332409\pi$
$360$		0			0
$361$	5.92010	+	10.2539i	0.311584	+	0.539680i
$362$	−37.4571	+	3.27707i	−1.96870	+	0.172239i
$363$		0			0
$364$	−7.22909	+	1.27468i	−0.378907	+	0.0668116i
$365$	−25.0068	−	19.1832i	−1.30891	−	1.00409i
$366$		0			0
$367$	−1.72794	−	19.7504i	−0.0901977	−	1.03096i	−0.897555	−	0.440902i	$-0.854659\pi$
$367$	−1.72794	−	19.7504i	−0.0901977	−	1.03096i	0.807357	−	0.590063i	$-0.200897\pi$
$368$	−0.200768	+	0.749277i	−0.0104658	+	0.0390588i
$369$		0			0
$370$	8.10668	−	12.7286i	0.421446	−	0.661728i
$371$	11.2070	+	30.7909i	0.581836	+	1.59858i
$372$		0			0
$373$	1.84840	−	21.1273i	0.0957063	−	1.09393i	−0.784754	−	0.619808i	$-0.787211\pi$
$373$	1.84840	−	21.1273i	0.0957063	−	1.09393i	0.880460	−	0.474120i	$-0.157234\pi$
$374$	−7.73714	−	2.81609i	−0.400078	−	0.145616i
$375$		0			0
$376$	5.83943	−	33.1170i	0.301145	−	1.70788i
$377$	0.830613	−	0.830613i	0.0427788	−	0.0427788i
$378$		0			0
$379$			4.95221i			0.254378i	0.991878	+	0.127189i	$0.0405955\pi$
$379$			4.95221i			0.254378i	−0.991878	+	0.127189i	$0.959405\pi$
$380$	13.6552	−	61.6325i	0.700497	−	3.16168i
$381$		0			0
$382$	2.90926	+	6.23894i	0.148851	+	0.319212i
$383$	28.1753	+	2.46502i	1.43969	+	0.125957i	0.780093	−	0.625663i	$-0.215172\pi$
$383$	28.1753	+	2.46502i	1.43969	+	0.125957i	0.659596	+	0.751620i	$0.270727\pi$
$384$		0			0
$385$	2.10927	−	4.05316i	0.107498	−	0.206568i
$386$	−32.8569	−	18.9699i	−1.67237	−	0.965545i
$387$		0			0
$388$	66.9484	+	17.9388i	3.39879	+	0.910703i
$389$	22.5434	+	18.9162i	1.14300	+	0.959088i	0.999533	−	0.0305681i	$-0.00973165\pi$
$389$	22.5434	+	18.9162i	1.14300	+	0.959088i	0.143463	+	0.989656i	$0.454176\pi$
$390$		0			0
$391$	0.0537524	+	0.304845i	0.00271838	+	0.0154167i
$392$	−16.6129	−	11.6325i	−0.839080	−	0.587530i
$393$		0			0
$394$	−14.2783	+	17.0163i	−0.719332	+	0.857267i
$395$	10.7581	−	5.60209i	0.541299	−	0.281872i
$396$		0			0
$397$	18.9334	−	5.07320i	0.950242	−	0.254616i	0.249777	−	0.968303i	$-0.419643\pi$
$397$	18.9334	−	5.07320i	0.950242	−	0.254616i	0.700465	+	0.713687i	$0.252976\pi$
$398$	−9.11662	−	4.25115i	−0.456975	−	0.213091i
$399$		0			0
$400$	−47.8128	+	33.4974i	−2.39064	+	1.67487i
$401$	0.0115561	−	0.0317502i	0.000577086	−	0.00158553i	−0.939404	−	0.342813i	$-0.888620\pi$
$401$	0.0115561	−	0.0317502i	0.000577086	−	0.00158553i	0.939981	+	0.341227i	$0.110843\pi$
$402$		0			0
$403$	0.505922	+	0.722531i	0.0252018	+	0.0359918i
$404$	−9.36163			−0.465759
$405$		0			0
$406$	20.5061			1.01770
$407$	−0.965702	−	1.37917i	−0.0478681	−	0.0683627i
$408$		0			0
$409$	−3.01485	+	8.28322i	−0.149075	+	0.409579i	−0.991643	−	0.129010i	$-0.958820\pi$
$409$	−3.01485	+	8.28322i	−0.149075	+	0.409579i	0.842569	+	0.538589i	$0.181042\pi$
$410$	−9.74789	−	1.28205i	−0.481414	−	0.0633157i
$411$		0			0
$412$	−75.2490	−	35.0892i	−3.70725	−	1.72872i
$413$	−13.5606	+	3.63355i	−0.667272	+	0.178795i
$414$		0			0
$415$	−3.81208	+	12.0959i	−0.187128	+	0.593762i
$416$	4.42180	−	5.26969i	0.216796	−	0.258368i
$417$		0			0
$418$	−8.03896	−	5.62894i	−0.393198	−	0.275320i
$419$	−5.75122	−	32.6168i	−0.280966	−	1.59344i	−0.719350	−	0.694648i	$-0.755560\pi$
$419$	−5.75122	−	32.6168i	−0.280966	−	1.59344i	0.438384	−	0.898788i	$-0.355551\pi$
$420$		0			0
$421$	12.7180	+	10.6716i	0.619835	+	0.520104i	0.897752	−	0.440502i	$-0.145199\pi$
$421$	12.7180	+	10.6716i	0.619835	+	0.520104i	−0.277916	+	0.960605i	$0.589644\pi$
$422$	−45.7728	−	12.2648i	−2.22819	−	0.597040i
$423$		0			0
$424$	−75.6750	−	43.6910i	−3.67510	−	2.12182i
$425$	−11.6429	+	20.1783i	−0.564765	+	0.978789i
$426$		0			0
$427$	−19.0708	−	1.66848i	−0.922901	−	0.0807433i
$428$	31.8660	+	68.3368i	1.54030	+	3.30318i
$429$		0			0
$430$	48.8145	+	10.8153i	2.35404	+	0.521558i
$431$		−	14.4385i		−	0.695480i	−0.937591	−	0.347740i	$-0.886949\pi$
$431$		−	14.4385i		−	0.695480i	0.937591	−	0.347740i	$-0.113051\pi$
$432$		0			0
$433$	16.4822	−	16.4822i	0.792085	−	0.792085i	−0.189748	−	0.981833i	$-0.560767\pi$
$433$	16.4822	−	16.4822i	0.792085	−	0.792085i	0.981833	+	0.189748i	$0.0607670\pi$
$434$	−2.67381	+	15.1640i	−0.128347	+	0.727893i
$435$		0			0
$436$	−44.6611	−	16.2553i	−2.13888	−	0.778488i
$437$	−0.0321562	+	0.367547i	−0.00153824	+	0.0175821i
$438$		0			0
$439$	10.9388	+	30.0541i	0.522080	+	1.43440i	0.868201	+	0.496213i	$0.165277\pi$
$439$	10.9388	+	30.0541i	0.522080	+	1.43440i	−0.346121	+	0.938190i	$0.612501\pi$
$440$	2.63883	+	11.8957i	0.125801	+	0.567105i
$441$		0			0
$442$	1.50592	−	5.62015i	0.0716291	−	0.267323i
$443$	1.56526	+	17.8910i	0.0743677	+	0.850027i	0.938165	+	0.346188i	$0.112524\pi$
$443$	1.56526	+	17.8910i	0.0743677	+	0.850027i	−0.863798	+	0.503839i	$0.831920\pi$
$444$		0			0
$445$	1.80043	+	13.6619i	0.0853487	+	0.647638i
$446$	−50.1811	+	8.84827i	−2.37614	+	0.418978i
$447$		0			0
$448$	48.0392	−	4.20289i	2.26964	−	0.198568i
$449$	−6.63475	−	11.4917i	−0.313113	−	0.542328i	0.665921	−	0.746022i	$-0.268039\pi$
$449$	−6.63475	−	11.4917i	−0.313113	−	0.542328i	−0.979035	+	0.203694i	$0.934705\pi$
$450$		0			0
$451$	−0.548456	+	0.949953i	−0.0258258	+	0.0447316i
$452$	44.6407	−	95.7323i	2.09972	−	4.50287i
$453$		0			0
$454$	−0.825948	−	0.984327i	−0.0387637	−	0.0461968i
$455$	2.98321	+	1.23523i	0.139855	+	0.0579086i
$456$		0			0
$457$	6.59496	−	4.61784i	0.308499	−	0.216013i	−0.409066	−	0.912505i	$-0.634145\pi$
$457$	6.59496	−	4.61784i	0.308499	−	0.216013i	0.717565	+	0.696491i	$0.245257\pi$
$458$	−28.2789	−	28.2789i	−1.32138	−	1.32138i
$459$		0			0
$460$	0.556732	−	0.510284i	0.0259578	−	0.0237921i
$461$	14.1578	+	2.49640i	0.659393	+	0.116269i	0.493324	−	0.869846i	$-0.335782\pi$
$461$	14.1578	+	2.49640i	0.659393	+	0.116269i	0.166068	+	0.986114i	$0.446893\pi$
$462$		0			0
$463$	18.8558	−	8.79261i	0.876304	−	0.408627i	0.0682032	−	0.997671i	$-0.478273\pi$
$463$	18.8558	−	8.79261i	0.876304	−	0.408627i	0.808101	+	0.589044i	$0.200496\pi$
$464$	−22.3922	+	18.7893i	−1.03953	+	0.872272i
$465$		0			0
$466$	1.38417	−	0.503795i	0.0641202	−	0.0233378i
$467$	6.38314	+	23.8222i	0.295376	+	1.10236i	0.940918	+	0.338635i	$0.109965\pi$
$467$	6.38314	+	23.8222i	0.295376	+	1.10236i	−0.645542	+	0.763725i	$0.723368\pi$
$468$		0			0
$469$	14.5849	−	8.42062i	0.673470	−	0.388828i
$470$	−16.4720	+	17.9808i	−0.759799	+	0.829391i
$471$		0			0
$472$	21.4739	−	30.6679i	0.988418	−	1.41161i
$473$	3.19951	−	4.56937i	0.147113	−	0.210100i
$474$		0			0
$475$	−19.6291	+	19.6393i	−0.900646	+	0.901114i
$476$	63.1279	−	36.4469i	2.89346	−	1.67054i
$477$		0			0
$478$	−3.90246	−	14.5642i	−0.178494	−	0.666150i
$479$	25.2593	−	9.19362i	1.15412	−	0.420067i	0.307130	−	0.951668i	$-0.400632\pi$
$479$	25.2593	−	9.19362i	1.15412	−	0.420067i	0.846995	+	0.531601i	$0.178409\pi$
$480$		0			0
$481$	0.911414	−	0.764768i	0.0415569	−	0.0348704i
$482$	4.41687	−	2.05962i	0.201183	−	0.0938132i
$483$		0			0
$484$	−52.8631	−	9.32118i	−2.40287	−	0.423690i
$485$	−20.5994	−	22.4744i	−0.935369	−	1.02051i
$486$		0			0
$487$	1.39406	+	1.39406i	0.0631711	+	0.0631711i	0.737987	−	0.674815i	$-0.235777\pi$
$487$	1.39406	+	1.39406i	0.0631711	+	0.0631711i	−0.674815	+	0.737987i	$0.735777\pi$
$488$	41.8191	−	29.2821i	1.89306	−	1.32554i
$489$		0			0
$490$	5.62967	+	13.5862i	0.254323	+	0.613764i
$491$	15.2423	+	18.1651i	0.687875	+	0.819777i	0.991097	−	0.133143i	$-0.0425068\pi$
$491$	15.2423	+	18.1651i	0.687875	+	0.819777i	−0.303222	+	0.952920i	$0.598062\pi$
$492$		0			0
$493$	−4.92970	+	10.5718i	−0.222023	+	0.476129i
$494$	3.46749	−	6.00587i	0.156010	−	0.270217i
$495$		0			0
$496$	−10.9747	−	19.0087i	−0.492778	−	0.853516i
$497$	18.8702	−	1.65093i	0.846444	−	0.0740542i
$498$		0			0
$499$	−30.8900	+	5.44673i	−1.38282	+	0.243829i	−0.815067	−	0.579366i	$-0.803300\pi$
$499$	−30.8900	+	5.44673i	−1.38282	+	0.243829i	−0.567758	+	0.823196i	$0.692189\pi$
$500$	56.7814	−	2.50130i	2.53934	−	0.111862i
$501$		0			0
$502$	4.51248	+	51.5779i	0.201402	+	2.30204i
$503$	1.59547	−	5.95437i	0.0711385	−	0.265492i	−0.921192	−	0.389109i	$-0.872783\pi$
$503$	1.59547	−	5.95437i	0.0711385	−	0.265492i	0.992330	+	0.123617i	$0.0394495\pi$
$504$		0			0
$505$	3.47320	+	2.21204i	0.154555	+	0.0984344i
$506$	−0.0401548	−	0.110325i	−0.00178510	−	0.00490452i
$507$		0			0
$508$	−3.37332	+	38.5572i	−0.149667	+	1.71070i
$509$	18.3832	+	6.69092i	0.814819	+	0.296570i	0.715613	−	0.698497i	$-0.246147\pi$
$509$	18.3832	+	6.69092i	0.814819	+	0.296570i	0.0992061	+	0.995067i	$0.468370\pi$
$510$		0			0
$511$	7.53240	−	42.7184i	0.333214	−	1.88975i
$512$	14.4712	−	14.4712i	0.639545	−	0.639545i
$513$		0			0
$514$			79.6382i			3.51269i
$515$	19.6265	+	30.7986i	0.864847	+	1.35715i
$516$		0			0
$517$	1.14977	+	2.46569i	0.0505668	+	0.108441i
$518$	20.6907	+	1.81020i	0.909097	+	0.0795357i
$519$		0			0
$520$	−8.21169	+	2.59031i	−0.360106	+	0.113593i
$521$	−1.02507	−	0.591824i	−0.0449091	−	0.0259283i	0.477377	−	0.878698i	$-0.341587\pi$
$521$	−1.02507	−	0.591824i	−0.0449091	−	0.0259283i	−0.522286	+	0.852770i	$0.674921\pi$
$522$		0			0
$523$	43.1925	+	11.5734i	1.88868	+	0.506069i	0.998751	+	0.0499636i	$0.0159105\pi$
$523$	43.1925	+	11.5734i	1.88868	+	0.506069i	0.889926	+	0.456106i	$0.150756\pi$
$524$	−45.7023	−	38.3488i	−1.99652	−	1.67528i
$525$		0			0
$526$	−3.87963	−	22.0025i	−0.169160	−	0.959354i
$527$	−7.17489	−	5.02391i	−0.312543	−	0.218845i
$528$		0			0
$529$	14.7813	−	17.6156i	0.642664	−	0.765897i
$530$	29.2659	+	56.2014i	1.27123	+	2.44123i
$531$		0			0
$532$	83.9219	−	22.4868i	3.63848	−	0.974927i
$533$	−0.702518	−	0.327589i	−0.0304294	−	0.0141895i
$534$		0			0
$535$	4.32474	−	32.8827i	0.186975	−	1.42164i
$536$	−15.3607	+	42.2032i	−0.663482	+	1.82290i
$537$		0			0
$538$	−3.38206	−	4.83008i	−0.145811	−	0.208240i
$539$	1.64076			0.0706724
$540$		0			0
$541$	−0.781277			−0.0335897			−0.0167949	−	0.999859i	$-0.505346\pi$
$541$	−0.781277			−0.0335897			−0.0167949	+	0.999859i	$0.505346\pi$
$542$	−8.97207	−	12.8134i	−0.385383	−	0.550384i
$543$		0			0
$544$	−23.3637	+	64.1912i	−1.00171	+	2.75218i
$545$	12.7285	+	16.5836i	0.545229	+	0.710365i
$546$		0			0
$547$	−10.0522	−	4.68743i	−0.429802	−	0.200420i	0.195665	−	0.980671i	$-0.437314\pi$
$547$	−10.0522	−	4.68743i	−0.429802	−	0.200420i	−0.625467	+	0.780251i	$0.715091\pi$
$548$	33.0149	−	8.84632i	1.41033	−	0.377896i
$549$		0			0
$550$	3.01987	−	8.30373i	0.128768	−	0.354072i
$551$	−8.93677	+	10.6504i	−0.380719	+	0.453724i
$552$		0			0
$553$	13.6747	+	9.57510i	0.581505	+	0.407175i
$554$	5.22900	+	29.6551i	0.222159	+	1.25993i
$555$		0			0
$556$	5.91335	+	4.96189i	0.250782	+	0.210431i
$557$	−13.0192	−	3.48849i	−0.551642	−	0.147812i	−0.0277782	−	0.999614i	$-0.508843\pi$
$557$	−13.0192	−	3.48849i	−0.551642	−	0.147812i	−0.523864	+	0.851802i	$0.675510\pi$
$558$		0			0
$559$	3.41375	+	1.97093i	0.144386	+	0.0833615i
$560$	−71.2743	−	37.0913i	−3.01189	−	1.56739i
$561$		0			0
$562$	−57.6316	−	5.04211i	−2.43104	−	0.212689i
$563$	−15.8881	−	34.0720i	−0.669601	−	1.43596i	−0.887878	−	0.460078i	$-0.847821\pi$
$563$	−15.8881	−	34.0720i	−0.669601	−	1.43596i	0.218277	−	0.975887i	$-0.429956\pi$
$564$		0			0
$565$	−39.1822	+	24.9690i	−1.64841	+	1.05045i
$566$			34.9323i			1.46831i
$567$		0			0
$568$	−35.7193	+	35.7193i	−1.49875	+	1.49875i
$569$	2.09817	−	11.8993i	0.0879598	−	0.498845i	−0.908719	−	0.417409i	$-0.862938\pi$
$569$	2.09817	−	11.8993i	0.0879598	−	0.498845i	0.996679	−	0.0814360i	$-0.0259506\pi$
$570$		0			0
$571$	0.672547	+	0.244787i	0.0281452	+	0.0102440i	0.356054	−	0.934465i	$-0.384122\pi$
$571$	0.672547	+	0.244787i	0.0281452	+	0.0102440i	−0.327909	+	0.944709i	$0.606344\pi$
$572$	−0.138031	+	1.57770i	−0.00577137	+	0.0659670i
$573$		0			0
$574$	−4.62809	−	12.7156i	−0.193173	−	0.530738i
$575$	−0.327123	+	0.0577683i	−0.0136420	+	0.00240910i
$576$		0			0
$577$	9.67417	−	36.1045i	0.402741	−	1.50305i	−0.405443	−	0.914120i	$-0.632883\pi$
$577$	9.67417	−	36.1045i	0.402741	−	1.50305i	0.808184	−	0.588930i	$-0.200451\pi$
$578$	1.09228	+	12.4848i	0.0454328	+	0.519300i
$579$		0			0
$580$	28.2145	−	3.71824i	1.17154	−	0.154392i
$581$	−17.1896	+	3.03100i	−0.713146	+	0.125747i
$582$		0			0
$583$	7.04253	−	0.616142i	0.291672	−	0.0255180i
$584$	57.8388	+	100.180i	2.39339	+	4.14547i
$585$		0			0
$586$	5.67358	−	9.82693i	0.234373	−	0.405947i
$587$	−3.89170	+	8.34577i	−0.160628	+	0.344467i	−0.970106	−	0.242683i	$-0.921972\pi$
$587$	−3.89170	+	8.34577i	−0.160628	+	0.344467i	0.809478	+	0.587150i	$0.199750\pi$
$588$		0			0
$589$	−6.71056	−	7.99734i	−0.276504	−	0.329525i
$590$	−25.0806	+	10.3925i	−1.03255	+	0.427854i
$591$		0			0
$592$	−24.2525	+	16.9818i	−0.996771	+	0.697946i
$593$	9.96484	+	9.96484i	0.409207	+	0.409207i	0.881462	−	0.472255i	$-0.156560\pi$
$593$	9.96484	+	9.96484i	0.409207	+	0.409207i	−0.472255	+	0.881462i	$0.656560\pi$
$594$		0			0
$595$	−32.0326	−	1.39441i	−1.31321	−	0.0571651i
$596$	−106.595	−	18.7957i	−4.36632	−	0.769900i
$597$		0			0
$598$	0.0751920	−	0.0350626i	0.00307483	−	0.00143382i
$599$	−5.73610	+	4.81316i	−0.234371	+	0.196660i	−0.752407	−	0.658698i	$-0.771107\pi$
$599$	−5.73610	+	4.81316i	−0.234371	+	0.196660i	0.518037	+	0.855358i	$0.326663\pi$
$600$		0			0
$601$	−20.4882	+	7.45708i	−0.835730	+	0.304181i	−0.724208	−	0.689581i	$-0.757795\pi$
$601$	−20.4882	+	7.45708i	−0.835730	+	0.304181i	−0.111522	+	0.993762i	$0.535572\pi$
$602$	17.8101	+	66.4682i	0.725886	+	2.70904i
$603$		0			0
$604$	−34.9543	+	20.1809i	−1.42227	+	0.821148i
$605$	17.4099	+	15.9491i	0.707813	+	0.648422i
$606$		0			0
$607$	13.1267	−	18.7469i	0.532796	−	0.760912i	−0.459042	−	0.888415i	$-0.651807\pi$
$607$	13.1267	−	18.7469i	0.532796	−	0.760912i	0.991838	+	0.127503i	$0.0406961\pi$
$608$	−46.7005	+	66.6953i	−1.89396	+	2.70485i
$609$		0			0
$610$	−36.9845	+	1.61959i	−1.49746	+	0.0655754i
$611$	−1.66496	+	0.961264i	−0.0673570	+	0.0388886i
$612$		0			0
$613$	3.87633	+	14.4667i	0.156564	+	0.584303i	0.998966	+	0.0454549i	$0.0144737\pi$
$613$	3.87633	+	14.4667i	0.156564	+	0.584303i	−0.842403	+	0.538848i	$0.818860\pi$
$614$	−46.5944	+	16.9590i	−1.88040	+	0.684409i
$615$		0			0
$616$	−12.8467	+	10.7796i	−0.517607	+	0.434324i
$617$	0.430054	−	0.200538i	0.0173133	−	0.00807334i	−0.413942	−	0.910303i	$-0.635848\pi$
$617$	0.430054	−	0.200538i	0.0173133	−	0.00807334i	0.431256	+	0.902230i	$0.358071\pi$
$618$		0			0
$619$	10.1152	+	1.78359i	0.406565	+	0.0716885i	0.373191	−	0.927754i	$-0.378264\pi$
$619$	10.1152	+	1.78359i	0.406565	+	0.0716885i	0.0333743	+	0.999443i	$0.489375\pi$
$620$	−0.929342	+	21.3491i	−0.0373233	+	0.857399i
$621$		0			0
$622$	15.4321	+	15.4321i	0.618770	+	0.618770i
$623$	−15.5357	+	10.8782i	−0.622425	+	0.435827i
$624$		0			0
$625$	−21.6571	−	12.4887i	−0.866285	−	0.499550i
$626$	−32.6187	−	38.8735i	−1.30371	−	1.55370i
$627$		0			0
$628$	29.3733	−	62.9913i	1.17212	−	2.51363i
$629$	−5.90732	+	10.2318i	−0.235540	+	0.407968i
$630$		0			0
$631$	−6.48152	−	11.2263i	−0.258025	−	0.446913i	0.707688	−	0.706526i	$-0.249738\pi$
$631$	−6.48152	−	11.2263i	−0.258025	−	0.446913i	−0.965713	+	0.259613i	$0.916405\pi$
$632$	−44.3488	+	3.88002i	−1.76410	+	0.154339i
$633$		0			0
$634$	44.5080	−	7.84797i	1.76764	−	0.311683i
$635$	10.3621	−	13.5078i	0.411208	−	0.536040i
$636$		0			0
$637$	0.101053	+	1.15504i	0.00400388	+	0.0457645i
$638$	1.14506	−	4.27341i	0.0453333	−	0.169186i
$639$		0			0
$640$	27.0288	−	5.99583i	1.06841	−	0.237006i
$641$	−16.0051	−	43.9737i	−0.632164	−	1.73686i	−0.675045	−	0.737777i	$-0.735876\pi$
$641$	−16.0051	−	43.9737i	−0.632164	−	1.73686i	0.0428806	−	0.999080i	$-0.486347\pi$
$642$		0			0
$643$	−1.93250	+	22.0886i	−0.0762103	+	0.871088i	0.857833	+	0.513928i	$0.171810\pi$
$643$	−1.93250	+	22.0886i	−0.0762103	+	0.871088i	−0.934043	+	0.357160i	$0.883745\pi$
$644$	0.976716	+	0.355496i	0.0384880	+	0.0140085i
$645$		0			0
$646$	−11.9584	+	67.8196i	−0.470498	+	2.66833i
$647$	−23.9696	+	23.9696i	−0.942341	+	0.942341i	−0.998426	−	0.0560849i	$-0.982138\pi$
$647$	−23.9696	+	23.9696i	−0.942341	+	0.942341i	0.0560849	+	0.998426i	$0.482138\pi$
$648$		0			0
$649$			3.02889i			0.118894i
$650$	6.03157	+	1.61448i	0.236578	+	0.0633249i
$651$		0			0
$652$	42.0693	+	90.2178i	1.64756	+	3.53320i
$653$	−9.67068	−	0.846075i	−0.378443	−	0.0331095i	−0.103652	−	0.994614i	$-0.533053\pi$
$653$	−9.67068	−	0.846075i	−0.378443	−	0.0331095i	−0.274791	+	0.961504i	$0.588609\pi$
$654$		0			0
$655$	7.89438	+	25.0264i	0.308459	+	0.977864i
$656$	16.7048	+	9.64453i	0.652214	+	0.376556i
$657$		0			0
$658$	−32.4179	−	8.68636i	−1.26378	−	0.338629i
$659$	−15.9731	−	13.4030i	−0.622224	−	0.522108i	0.276278	−	0.961078i	$-0.410899\pi$
$659$	−15.9731	−	13.4030i	−0.622224	−	0.522108i	−0.898502	+	0.438970i	$0.855343\pi$
$660$		0			0
$661$	−6.68365	−	37.9049i	−0.259964	−	1.47433i	−0.783002	−	0.622020i	$-0.786312\pi$
$661$	−6.68365	−	37.9049i	−0.259964	−	1.47433i	0.523038	−	0.852310i	$-0.324799\pi$
$662$	31.0096	+	21.7132i	1.20522	+	0.843906i
$663$		0			0
$664$	29.9205	−	35.6578i	1.16114	−	1.38379i
$665$	−36.4487	−	11.4870i	−1.41342	−	0.445447i
$666$		0			0
$667$	−0.160660	+	0.0430488i	−0.00622079	+	0.00166685i
$668$	101.236	+	47.2070i	3.91693	+	1.82649i
$669$		0			0
$670$	25.8350	−	19.8292i	0.998094	−	0.766070i
$671$	−1.41262	+	3.88114i	−0.0545335	+	0.149830i
$672$		0			0
$673$	−11.8077	−	16.8631i	−0.455153	−	0.650026i	0.524339	−	0.851510i	$-0.324313\pi$
$673$	−11.8077	−	16.8631i	−0.455153	−	0.650026i	−0.979492	+	0.201484i	$0.935424\pi$
$674$	−18.1379			−0.698646
$675$		0			0
$676$	64.9678			2.49876
$677$	−13.0007	−	18.5670i	−0.499659	−	0.713588i	0.487536	−	0.873103i	$-0.337896\pi$
$677$	−13.0007	−	18.5670i	−0.499659	−	0.713588i	−0.987195	+	0.159515i	$0.949007\pi$
$678$		0			0
$679$	14.3508	−	39.4285i	0.550734	−	1.51313i
$680$	67.8286	−	52.0607i	2.60111	−	1.99644i
$681$		0			0
$682$	3.01082	+	1.40397i	0.115290	+	0.0537608i
$683$	−7.91835	+	2.12172i	−0.302987	+	0.0811852i	−0.407110	−	0.913379i	$-0.633463\pi$
$683$	−7.91835	+	2.12172i	−0.302987	+	0.0811852i	0.104122	+	0.994564i	$0.466797\pi$
$684$		0			0
$685$	−14.3389	−	4.51900i	−0.547862	−	0.172662i
$686$	23.8444	−	28.4166i	0.910382	−	1.08495i
$687$		0			0
$688$	−80.3518	−	56.2630i	−3.06338	−	2.14500i
$689$	0.867490	+	4.91978i	0.0330487	+	0.187429i
$690$		0			0
$691$	2.09562	+	1.75844i	0.0797212	+	0.0668941i	0.681777	−	0.731560i	$-0.261207\pi$
$691$	2.09562	+	1.75844i	0.0797212	+	0.0668941i	−0.602056	+	0.798454i	$0.705652\pi$
$692$	−18.4268	−	4.93744i	−0.700481	−	0.187693i
$693$		0			0
$694$	31.6991	+	18.3015i	1.20328	+	0.694715i
$695$	−1.02144	−	3.23813i	−0.0387455	−	0.122829i
$696$		0			0
$697$	7.66804	+	0.670867i	0.290448	+	0.0254109i
$698$	−30.0939	−	64.5366i	−1.13907	−	2.44275i
$699$		0			0
$700$	39.1299	+	67.7343i	1.47897	+	2.56011i
$701$		−	45.2015i		−	1.70724i	−0.520899	−	0.853618i	$-0.674403\pi$
$701$		−	45.2015i		−	1.70724i	0.520899	−	0.853618i	$-0.325597\pi$
$702$		0			0
$703$	−9.95741	+	9.95741i	−0.375551	+	0.375551i
$704$	1.80664	−	10.2459i	0.0680901	−	0.386158i
$705$		0			0
$706$	0.118329	+	0.0430682i	0.00445337	+	0.00162089i
$707$	−0.493942	+	5.64579i	−0.0185766	+	0.212332i
$708$		0			0
$709$	6.90171	+	18.9623i	0.259199	+	0.712144i	0.999217	+	0.0395569i	$0.0125946\pi$
$709$	6.90171	+	18.9623i	0.259199	+	0.712144i	−0.740018	+	0.672587i	$0.765183\pi$
$710$	35.7612	−	7.93295i	1.34210	−	0.297718i
$711$		0			0
$712$	13.0903	−	48.8536i	0.490579	−	1.83086i
$713$	−0.0108853	−	0.124419i	−0.000407656	−	0.00465953i
$714$		0			0
$715$	0.424001	−	0.552718i	0.0158567	−	0.0206705i
$716$	72.2265	−	12.7355i	2.69923	−	0.475947i
$717$		0			0
$718$	−49.9836	+	4.37300i	−1.86537	+	0.163199i
$719$	18.2157	+	31.5505i	0.679331	+	1.17664i	0.975183	+	0.221402i	$0.0710631\pi$
$719$	18.2157	+	31.5505i	0.679331	+	1.17664i	−0.295852	+	0.955234i	$0.595604\pi$
$720$		0			0
$721$	−25.1318	+	43.5295i	−0.935957	+	1.62113i
$722$	−13.3179	+	28.5603i	−0.495640	+	1.06290i
$723$		0			0
$724$	−46.1638	−	55.0159i	−1.71566	−	2.04465i
$725$	−11.3463	−	5.28726i	−0.421390	−	0.196364i
$726$		0			0
$727$	10.9561	−	7.67153i	0.406338	−	0.284521i	−0.352485	−	0.935817i	$-0.614663\pi$
$727$	10.9561	−	7.67153i	0.406338	−	0.284521i	0.758824	+	0.651296i	$0.225774\pi$
$728$	−8.37976	−	8.37976i	−0.310575	−	0.310575i
$729$		0			0
$730$	3.64805	−	83.8038i	0.135020	−	3.10172i
$731$	−38.5489	−	6.79721i	−1.42578	−	0.251404i
$732$		0			0
$733$	−38.0568	+	17.7462i	−1.40566	+	0.655470i	−0.969656	−	0.244474i	$-0.921385\pi$
$733$	−38.0568	+	17.7462i	−1.40566	+	0.655470i	−0.436005	+	0.899944i	$0.643607\pi$
$734$	40.4216	−	33.9178i	1.49199	−	1.25193i
$735$		0			0
$736$	−0.915308	+	0.333145i	−0.0337387	+	0.0122799i
$737$	−0.940413	−	3.50967i	−0.0346406	−	0.129280i
$738$		0			0
$739$	−34.0711	+	19.6709i	−1.25332	+	0.723607i	−0.971768	−	0.235938i	$-0.924184\pi$
$739$	−34.0711	+	19.6709i	−1.25332	+	0.723607i	−0.281556	+	0.959545i	$0.590850\pi$
$740$	28.7968	−	1.26104i	1.05859	−	0.0463569i
$741$		0			0
$742$	−50.0213	+	71.4378i	−1.83634	+	2.62256i
$743$	−7.43173	+	10.6136i	−0.272644	+	0.389376i	−0.932002	−	0.362453i	$-0.881939\pi$
$743$	−7.43173	+	10.6136i	−0.272644	+	0.389376i	0.659358	+	0.751829i	$0.270828\pi$
$744$		0			0
$745$	35.1061	+	32.1604i	1.28619	+	1.17827i
$746$	48.8829	−	28.2225i	1.78973	−	1.03330i
$747$		0			0
$748$	−4.07039	−	15.1909i	−0.148828	−	0.555434i
$749$	42.8937	−	15.6120i	1.56730	−	0.570451i
$750$		0			0
$751$	30.6700	−	25.7352i	1.11916	−	0.939089i	0.120601	−	0.992701i	$-0.461518\pi$
$751$	30.6700	−	25.7352i	1.11916	−	0.939089i	0.998562	+	0.0536119i	$0.0170734\pi$
$752$	43.3589	−	20.2186i	1.58114	−	0.737296i
$753$		0			0
$754$	3.07888	+	0.542889i	0.112126	+	0.0197709i
$755$	17.7367	+	0.772091i	0.645503	+	0.0280993i
$756$		0			0
$757$	0.846964	+	0.846964i	0.0307834	+	0.0307834i	0.722331	−	0.691548i	$-0.243071\pi$
$757$	0.846964	+	0.846964i	0.0307834	+	0.0307834i	−0.691548	+	0.722331i	$0.743071\pi$
$758$	−10.7967	+	7.55993i	−0.392154	+	0.274589i
$759$		0			0
$760$	94.1504	−	39.0127i	3.41519	−	1.41514i
$761$	3.25980	+	3.88488i	0.118168	+	0.140827i	0.821885	−	0.569653i	$-0.192922\pi$
$761$	3.25980	+	3.88488i	0.118168	+	0.140827i	−0.703718	+	0.710480i	$0.748478\pi$
$762$		0			0
$763$	−12.1596	+	26.0764i	−0.440208	+	0.944029i
$764$	−6.57430	+	11.3870i	−0.237850	+	0.411968i
$765$		0			0
$766$	37.6375	+	65.1901i	1.35990	+	2.35542i
$767$	−2.13224	+	0.186547i	−0.0769909	+	0.00673583i
$768$		0			0
$769$	−26.0795	+	4.59852i	−0.940451	+	0.165827i	−0.622800	−	0.782381i	$-0.714005\pi$
$769$	−26.0795	+	4.59852i	−0.940451	+	0.165827i	−0.317651	+	0.948208i	$0.602894\pi$
$770$	12.0566	−	1.58887i	0.434488	−	0.0572589i
$771$		0			0
$772$	−6.31593	−	72.1914i	−0.227315	−	2.59822i
$773$	2.81189	−	10.4941i	0.101137	−	0.377447i	−0.896742	−	0.442555i	$-0.854072\pi$
$773$	2.81189	−	10.4941i	0.101137	−	0.377447i	0.997878	+	0.0651074i	$0.0207390\pi$
$774$		0			0
$775$	5.38931	−	7.70099i	0.193590	−	0.276628i
$776$	38.2703	+	105.147i	1.37383	+	3.77455i
$777$		0			0
$778$	−6.82635	+	78.0256i	−0.244737	+	2.79735i
$779$	8.62118	+	3.13785i	0.308886	+	0.112425i
$780$		0			0
$781$	0.709661	−	4.02469i	0.0253937	−	0.144015i
$782$	−0.582559	+	0.582559i	−0.0208323	+	0.0208323i
$783$		0			0
$784$		−	28.8525i		−	1.03045i
$785$	−25.7817	+	16.4294i	−0.920187	+	0.586392i
$786$		0			0
$787$	3.36829	+	7.22332i	0.120067	+	0.257484i	0.957151	−	0.289591i	$-0.0935192\pi$
$787$	3.36829	+	7.22332i	0.120067	+	0.257484i	−0.837084	+	0.547074i	$0.815741\pi$
$788$	−42.2668	−	3.69786i	−1.50569	−	0.131731i
$789$		0			0
$790$	28.6366	+	14.9025i	1.01884	+	0.530209i
$791$	−55.3786	−	31.9729i	−1.96904	−	1.13682i
$792$		0			0
$793$	−2.81921	−	0.755404i	−0.100113	−	0.0268252i
$794$	39.9638	+	33.5336i	1.41826	+	1.19006i
$795$		0			0
$796$	−3.33636	−	18.9215i	−0.118254	−	0.670653i
$797$	0.621792	+	0.435383i	0.0220250	+	0.0154221i	0.584537	−	0.811367i	$-0.301276\pi$
$797$	0.621792	+	0.435383i	0.0220250	+	0.0154221i	−0.562512	+	0.826789i	$0.690165\pi$
$798$		0			0
$799$	12.2715	−	14.6246i	0.434136	−	0.517383i
$800$	−68.8920	−	25.0544i	−2.43570	−	0.885806i
$801$		0			0
$802$	0.0868625	−	0.0232747i	0.00306722	−	0.000821859i
$803$	−8.48179	−	3.95512i	−0.299316	−	0.139573i
$804$		0			0
$805$	−0.278366	−	0.362676i	−0.00981111	−	0.0127827i
$806$	−0.802918	+	2.20600i	−0.0282816	+	0.0777030i
$807$		0			0
$808$	−8.66877	−	12.3803i	−0.304966	−	0.435537i
$809$	−3.88327			−0.136528			−0.0682642	−	0.997667i	$-0.521746\pi$
$809$	−3.88327			−0.136528			−0.0682642	+	0.997667i	$0.521746\pi$
$810$		0			0
$811$	−22.9810			−0.806974			−0.403487	−	0.914985i	$-0.632202\pi$
$811$	−22.9810			−0.806974			−0.403487	+	0.914985i	$0.632202\pi$
$812$	22.4656	+	32.0843i	0.788390	+	1.12594i
$813$		0			0
$814$	1.53261	−	4.21081i	0.0537179	−	0.147589i
$815$	5.70950	−	43.4116i	0.199995	−	1.52064i
$816$		0			0
$817$	−42.2840	−	19.7174i	−1.47933	−	0.689824i
$818$	−22.6613	+	6.07207i	−0.792333	+	0.212305i
$819$		0			0
$820$	−8.67348	−	16.6563i	−0.302891	−	0.581664i
$821$	1.59034	−	1.89529i	0.0555031	−	0.0661461i	−0.737579	−	0.675261i	$-0.764031\pi$
$821$	1.59034	−	1.89529i	0.0555031	−	0.0661461i	0.793082	+	0.609115i	$0.208475\pi$
$822$		0			0
$823$	26.9245	+	18.8527i	0.938528	+	0.657164i	0.939396	−	0.342835i	$-0.111387\pi$
$823$	26.9245	+	18.8527i	0.938528	+	0.657164i	−0.000867529		1.00000i	$0.500276\pi$
$824$	−23.2761	−	132.005i	−0.810860	−	4.59862i
$825$		0			0
$826$	−28.6230	−	24.0176i	−0.995923	−	0.835678i
$827$	−8.32126	−	2.22968i	−0.289359	−	0.0775334i	0.111220	−	0.993796i	$-0.464524\pi$
$827$	−8.32126	−	2.22968i	−0.289359	−	0.0775334i	−0.400579	+	0.916262i	$0.631191\pi$
$828$		0			0
$829$	7.38409	+	4.26321i	0.256460	+	0.148067i	0.622719	−	0.782446i	$-0.286028\pi$
$829$	7.38409	+	4.26321i	0.256460	+	0.148067i	−0.366259	+	0.930513i	$0.619361\pi$
$830$	−32.1905	+	10.1542i	−1.11735	+	0.352459i
$831$		0			0
$832$	7.32410	+	0.640776i	0.253918	+	0.0222149i
$833$	−4.86588	−	10.4349i	−0.168593	−	0.361548i
$834$		0			0
$835$	−26.4044	−	41.4347i	−0.913761	−	1.43391i
$836$		−	18.7448i		−	0.648301i
$837$		0			0
$838$	62.3307	−	62.3307i	2.15318	−	2.15318i
$839$	8.06541	−	45.7412i	0.278449	−	1.57916i	−0.449340	−	0.893361i	$-0.648341\pi$
$839$	8.06541	−	45.7412i	0.278449	−	1.57916i	0.727789	−	0.685802i	$-0.240548\pi$
$840$		0			0
$841$	21.3614	+	7.77490i	0.736599	+	0.268100i
$842$	−3.85112	+	44.0185i	−0.132718	+	1.51698i
$843$		0			0
$844$	−30.9571	−	85.0539i	−1.06559	−	2.92768i
$845$	−24.1033	−	15.3511i	−0.829178	−	0.528093i
$846$		0			0
$847$	−8.41058	+	31.3887i	−0.288991	+	1.07853i
$848$	−10.8348	−	123.842i	−0.372068	−	4.25276i
$849$		0			0
$850$	−61.7660	+	5.42000i	−2.11856	+	0.185904i
$851$	−0.165907	+	0.0292538i	−0.00568721	+	0.00100281i
$852$		0			0
$853$	20.6498	−	1.80662i	0.707035	−	0.0618575i	0.272034	−	0.962288i	$-0.412304\pi$
$853$	20.6498	−	1.80662i	0.707035	−	0.0618575i	0.435001	+	0.900430i	$0.356748\pi$
$854$	−25.4755	−	44.1248i	−0.871752	−	1.50992i
$855$		0			0
$856$	−60.8644	+	105.420i	−2.08030	+	3.60319i
$857$	1.85929	−	3.98725i	0.0635120	−	0.136202i	−0.871990	−	0.489524i	$-0.837170\pi$
$857$	1.85929	−	3.98725i	0.0635120	−	0.136202i	0.935502	+	0.353322i	$0.114948\pi$
$858$		0			0
$859$	27.5782	+	32.8664i	0.940956	+	1.12139i	0.992442	+	0.122714i	$0.0391598\pi$
$859$	27.5782	+	32.8664i	0.940956	+	1.12139i	−0.0514862	+	0.998674i	$0.516396\pi$
$860$	36.5574	+	88.2249i	1.24660	+	3.00845i
$861$		0			0
$862$	31.4786	−	22.0415i	1.07217	−	0.750738i
$863$	29.7115	+	29.7115i	1.01139	+	1.01139i	0.999934	+	0.0114553i	$0.00364642\pi$
$863$	29.7115	+	29.7115i	1.01139	+	1.01139i	0.0114553	+	0.999934i	$0.496354\pi$
$864$		0			0
$865$	5.66974	+	6.18582i	0.192777	+	0.210324i
$866$	61.0955	+	10.7728i	2.07611	+	0.366074i
$867$		0			0
$868$	−26.6552	+	12.4295i	−0.904736	+	0.421885i
$869$	2.75902	−	2.31509i	0.0935932	−	0.0785340i
$870$		0			0
$871$	2.41278	−	0.878181i	0.0817540	−	0.0297560i
$872$	−19.8588	−	74.1142i	−0.672505	−	2.50982i
$873$		0			0
$874$	−0.850406	+	0.490982i	−0.0287654	+	0.0166077i
$875$	1.48745	−	34.3755i	0.0502848	−	1.16211i
$876$		0			0
$877$	6.63310	−	9.47306i	0.223984	−	0.319882i	−0.691394	−	0.722478i	$-0.743003\pi$
$877$	6.63310	−	9.47306i	0.223984	−	0.319882i	0.915378	+	0.402596i	$0.131892\pi$
$878$	−48.8243	+	69.7284i	−1.64774	+	2.35322i
$879$		0			0
$880$	−11.7097	+	12.7822i	−0.394733	+	0.430888i
$881$	−12.7653	+	7.37007i	−0.430075	+	0.248304i	−0.699379	−	0.714751i	$-0.746540\pi$
$881$	−12.7653	+	7.37007i	−0.430075	+	0.248304i	0.269304	+	0.963055i	$0.413206\pi$
$882$		0			0
$883$	4.11349	+	15.3517i	0.138430	+	0.516627i	0.999960	+	0.00892106i	$0.00283970\pi$
$883$	4.11349	+	15.3517i	0.138430	+	0.516627i	−0.861530	+	0.507706i	$0.830494\pi$
$884$	10.4432	−	3.80103i	0.351244	−	0.127842i
$885$		0			0
$886$	−36.6160	+	30.7245i	−1.23014	+	1.03221i
$887$	6.76369	−	3.15396i	0.227102	−	0.105900i	−0.305737	−	0.952116i	$-0.598903\pi$
$887$	6.76369	−	3.15396i	0.227102	−	0.105900i	0.532839	+	0.846216i	$0.321125\pi$
$888$		0			0
$889$	23.0750	+	4.06875i	0.773911	+	0.136461i
$890$	−27.0369	+	24.7812i	−0.906280	+	0.830669i
$891$		0			0
$892$	−68.8206	−	68.8206i	−2.30428	−	2.30428i
$893$	18.6396	−	13.0516i	0.623750	−	0.436755i
$894$		0			0
$895$	−29.8055	−	12.3413i	−0.996288	−	0.412524i
$896$	24.4930	+	29.1896i	0.818253	+	0.975156i
$897$		0			0
$898$	14.9255	−	32.0079i	0.498072	−	1.06812i
$899$	2.35319	−	4.07585i	0.0784834	−	0.135937i
$900$		0			0
$901$	−24.8041	−	42.9619i	−0.826344	−	1.43127i
$902$	−2.90833	+	0.254446i	−0.0968367	+	0.00847211i
$903$		0			0
$904$	167.938	−	29.6120i	5.58553	−	0.984880i
$905$	4.12737	+	31.3190i	0.137198	+	1.04108i
$906$		0			0
$907$	1.42792	+	16.3212i	0.0474134	+	0.541937i	0.982341	+	0.187099i	$0.0599085\pi$
$907$	1.42792	+	16.3212i	0.0474134	+	0.541937i	−0.934928	+	0.354838i	$0.884536\pi$
$908$	0.635223	−	2.37069i	0.0210806	−	0.0786740i
$909$		0			0
$910$	1.86107	+	8.38960i	0.0616940	+	0.278113i
$911$	0.825532	+	2.26813i	0.0273511	+	0.0751465i	0.952617	−	0.304173i	$-0.0983802\pi$
$911$	0.825532	+	2.26813i	0.0273511	+	0.0751465i	−0.925266	+	0.379320i	$0.876158\pi$
$912$		0			0
$913$	−0.328216	+	3.75152i	−0.0108624	+	0.124157i
$914$	20.1354	+	7.32869i	0.666020	+	0.242412i
$915$		0			0
$916$	13.2645	−	75.2269i	0.438273	−	2.48557i
$917$	−25.5387	+	25.5387i	−0.843361	+	0.843361i
$918$		0			0
$919$		−	5.68243i		−	0.187446i	−0.995598	−	0.0937230i	$-0.970123\pi$
$919$		−	5.68243i		−	0.187446i	0.995598	−	0.0937230i	$-0.0298768\pi$
$920$	1.19035	+	0.263732i	0.0392447	+	0.00869500i
$921$		0			0
$922$	16.1703	+	34.6774i	0.532541	+	1.14204i
$923$	2.87697	+	0.251702i	0.0946965	+	0.00828487i
$924$		0			0
$925$	−10.9817	−	6.33647i	−0.361075	−	0.208342i
$926$	47.9543	+	27.6864i	1.57588	+	0.909832i
$927$		0			0
$928$	−35.4544	−	9.49998i	−1.16385	−	0.311852i
$929$	−31.5686	−	26.4892i	−1.03573	−	0.869082i	−0.0442093	−	0.999022i	$-0.514077\pi$
$929$	−31.5686	−	26.4892i	−1.03573	−	0.869082i	−0.991522	+	0.129941i	$0.958521\pi$
$930$		0			0
$931$	−2.38300	−	13.5147i	−0.0780996	−	0.442925i
$932$	2.30468	+	1.61376i	0.0754924	+	0.0528604i
$933$		0			0
$934$	−42.1923	+	50.2828i	−1.38057	+	1.64530i
$935$	−2.07929	+	6.59765i	−0.0680001	+	0.215766i
$936$		0			0
$937$	7.80116	−	2.09031i	0.254853	−	0.0682876i	−0.129131	−	0.991628i	$-0.541219\pi$
$937$	7.80116	−	2.09031i	0.254853	−	0.0682876i	0.383983	+	0.923340i	$0.374552\pi$
$938$	40.6235	+	18.9430i	1.32640	+	0.618512i
$939$		0			0
$940$	−46.1792	−	6.07350i	−1.50620	−	0.198096i
$941$	−17.0461	+	46.8337i	−0.555686	+	1.52673i	0.270147	+	0.962819i	$0.412928\pi$
$941$	−17.0461	+	46.8337i	−0.555686	+	1.52673i	−0.825833	+	0.563915i	$0.809294\pi$
$942$		0			0
$943$	0.0629540	+	0.0899076i	0.00205006	+	0.00292780i
$944$	53.2626			1.73355
$945$		0			0
$946$	14.8463			0.482696
$947$	27.9030	+	39.8496i	0.906726	+	1.29494i	0.955153	+	0.296112i	$0.0956901\pi$
$947$	27.9030	+	39.8496i	0.906726	+	1.29494i	−0.0484276	+	0.998827i	$0.515421\pi$
$948$		0			0
$949$	2.26190	−	6.21452i	0.0734244	−	0.201732i
$950$	−72.7825	−	12.8140i	−2.36138	−	0.415742i
$951$		0			0
$952$	106.655	+	49.7340i	3.45671	+	1.61189i
$953$	48.5541	−	13.0100i	1.57282	−	0.421436i	0.636127	−	0.771584i	$-0.280535\pi$
$953$	48.5541	−	13.0100i	1.57282	−	0.421436i	0.936694	+	0.350148i	$0.113869\pi$
$954$		0			0
$955$	5.12970	−	2.67120i	0.165993	−	0.0864380i
$956$	18.5120	−	22.0618i	0.598722	−	0.713529i
$957$		0			0
$958$	58.6039	+	41.0349i	1.89341	+	1.32578i
$959$	−3.59307	−	20.3773i	−0.116026	−	0.658017i
$960$		0			0
$961$	−21.0402	−	17.6548i	−0.678716	−	0.569510i
$962$	3.05867	+	0.819569i	0.0986156	+	0.0264240i
$963$		0			0
$964$	8.06148	+	4.65430i	0.259643	+	0.149905i
$965$	−14.7147	+	28.2756i	−0.473683	+	0.910224i
$966$		0			0
$967$	−49.5607	−	4.33600i	−1.59377	−	0.139436i	−0.744581	−	0.667533i	$-0.767350\pi$
$967$	−49.5607	−	4.33600i	−1.59377	−	0.139436i	−0.849185	+	0.528096i	$0.822906\pi$
$968$	−36.6238	−	78.5400i	−1.17713	−	2.52437i
$969$		0			0
$970$	17.5517	−	79.2192i	0.563550	−	2.54357i
$971$		−	40.2818i		−	1.29270i	−0.763039	−	0.646352i	$-0.776294\pi$
$971$		−	40.2818i		−	1.29270i	0.763039	−	0.646352i	$-0.223706\pi$
$972$		0			0
$973$	3.30441	−	3.30441i	0.105934	−	0.105934i
$974$	−0.911162	+	5.16745i	−0.0291955	+	0.165576i
$975$		0			0
$976$	68.2493	+	24.8407i	2.18461	+	0.795132i
$977$	−3.30670	+	37.7958i	−0.105791	+	1.20919i	0.738854	+	0.673866i	$0.235367\pi$
$977$	−3.30670	+	37.7958i	−0.105791	+	1.20919i	−0.844644	+	0.535328i	$0.820188\pi$
$978$		0			0
$979$	1.39948	+	3.84504i	0.0447276	+	0.122888i
$980$	−15.0897	+	23.6929i	−0.482022	+	0.756840i
$981$		0			0
$982$	−16.3345	+	60.9612i	−0.521255	+	1.94535i
$983$	−3.12235	−	35.6886i	−0.0995874	−	1.13829i	−0.867399	−	0.497614i	$-0.834210\pi$
$983$	−3.12235	−	35.6886i	−0.0995874	−	1.13829i	0.767811	−	0.640676i	$-0.221346\pi$
$984$		0			0
$985$	14.8074	+	11.3590i	0.471802	+	0.361929i
$986$	−30.5739	+	5.39101i	−0.973672	+	0.171685i
$987$		0			0
$988$	13.1958	−	1.15448i	0.419813	−	0.0367289i
$989$	−0.279076	−	0.483373i	−0.00887409	−	0.0153704i
$990$		0			0
$991$	21.8850	−	37.9060i	0.695201	−	1.20412i	−0.274912	−	0.961469i	$-0.588649\pi$
$991$	21.8850	−	37.9060i	0.695201	−	1.20412i	0.970113	−	0.242654i	$-0.0780179\pi$
$992$	11.6480	−	24.9793i	0.369826	−	0.793094i
$993$		0			0
$994$	32.4061	+	38.6201i	1.02786	+	1.22495i
$995$	−3.23310	+	7.80827i	−0.102496	+	0.247539i
$996$		0			0
$997$	−19.9603	+	13.9764i	−0.632150	+	0.442636i	−0.845233	−	0.534398i	$-0.820538\pi$
$997$	−19.9603	+	13.9764i	−0.632150	+	0.442636i	0.213083	+	0.977034i	$0.431649\pi$
$998$	−59.0307	−	59.0307i	−1.86859	−	1.86859i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.332.16		192
3.2	odd	2		135.2.q.a.2.1	✓	192
5.3	odd	4	inner	405.2.r.a.8.16		192
15.2	even	4		675.2.ba.b.218.16		192
15.8	even	4		135.2.q.a.83.1	yes	192
15.14	odd	2		675.2.ba.b.407.16		192
27.13	even	9		135.2.q.a.122.1	yes	192
27.14	odd	18	inner	405.2.r.a.152.16		192
135.13	odd	36		135.2.q.a.68.1	yes	192
135.67	odd	36		675.2.ba.b.68.16		192
135.68	even	36	inner	405.2.r.a.233.16		192
135.94	even	18		675.2.ba.b.257.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.1	✓	192	3.2	odd	2
135.2.q.a.68.1	yes	192	135.13	odd	36
135.2.q.a.83.1	yes	192	15.8	even	4
135.2.q.a.122.1	yes	192	27.13	even	9
405.2.r.a.8.16		192	5.3	odd	4	inner
405.2.r.a.152.16		192	27.14	odd	18	inner
405.2.r.a.233.16		192	135.68	even	36	inner
405.2.r.a.332.16		192	1.1	even	1	trivial
675.2.ba.b.68.16		192	135.67	odd	36
675.2.ba.b.218.16		192	15.2	even	4
675.2.ba.b.257.16		192	135.94	even	18
675.2.ba.b.407.16		192	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.52658 + 2.18018i) q^{2} +(-1.73870 + 4.77703i) q^{4} +(1.77382 - 1.36146i) q^{5} +(2.78918 + 1.30062i) q^{7} +(-7.92739 + 2.12414i) q^{8} +(5.67609 + 1.78885i) q^{10} +(0.426793 - 0.508631i) q^{11} +(0.384347 + 0.269123i) q^{13} +(1.42232 + 8.06640i) q^{14} +(-8.94423 - 7.50510i) q^{16} +(-4.50051 - 1.20591i) q^{17} +(-4.80938 - 2.77670i) q^{19} +(3.41962 + 10.8407i) q^{20} +(1.76044 + 0.154018i) q^{22} +(-0.0280775 - 0.0602123i) q^{23} +(1.29284 - 4.82997i) q^{25} +1.24878i q^{26} +(-11.0626 + 11.0626i) q^{28} +(0.434735 - 2.46551i) q^{29} +(1.76652 + 0.642961i) q^{31} +(1.27781 - 14.6055i) q^{32} +(-4.24128 - 11.6528i) q^{34} +(6.71823 - 1.49031i) q^{35} +(0.656295 - 2.44933i) q^{37} +(-1.28820 - 14.7241i) q^{38} +(-11.1698 + 14.5607i) q^{40} +(-1.62695 + 0.286875i) q^{41} +(8.36925 - 0.732214i) q^{43} +(1.68769 + 2.92316i) q^{44} +(0.0884111 - 0.153133i) q^{46} +(-1.73166 + 3.71355i) q^{47} +(1.58841 + 1.89299i) q^{49} +(12.5038 - 4.55469i) q^{50} +(-1.95387 + 1.36812i) q^{52} +(7.52870 + 7.52870i) q^{53} +(0.0645683 - 1.48328i) q^{55} +(-24.8736 - 4.38589i) q^{56} +(6.03890 - 2.81598i) q^{58} +(-3.49452 + 2.93225i) q^{59} +(-5.84534 + 2.12753i) q^{61} +(1.29496 + 4.83286i) q^{62} +(13.5701 - 7.83468i) q^{64} +(1.04816 - 0.0459001i) q^{65} +(3.13881 - 4.48268i) q^{67} +(13.5857 - 19.4024i) q^{68} +(13.5050 + 12.3719i) q^{70} +(5.33043 - 3.07752i) q^{71} +(-3.64803 - 13.6146i) q^{73} +(6.34185 - 2.30824i) q^{74} +(21.6264 - 18.1467i) q^{76} +(1.85194 - 0.863572i) q^{77} +(5.34198 + 0.941936i) q^{79} +(-26.0833 - 1.13543i) q^{80} +(-3.10910 - 3.10910i) q^{82} +(-4.64599 + 3.25316i) q^{83} +(-9.62487 + 3.98822i) q^{85} +(14.3727 + 17.1287i) q^{86} +(-2.30295 + 4.93869i) q^{88} +(-3.08131 + 5.33699i) q^{89} +(0.721988 + 1.25052i) q^{91} +(0.336454 - 0.0294359i) q^{92} +(-10.7397 + 1.89370i) q^{94} +(-12.3113 + 1.62244i) q^{95} +(-1.18828 - 13.5821i) q^{97} +(-1.70223 + 6.35281i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

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